Newbetuts

Given three a-triangle-sidelengths $a,b,c$. Prove that $3\left((a^{2}b(a-b)+b^{2}c(b-c)+c^{2}a(c-a)\right)\geqq b(a+b-c)(a-c)(c-b)$ .

Proving that $\cos\frac{2\pi}{13}+\cos\frac{6\pi}{13}+\cos\frac{8\pi}{13}=\frac{\sqrt{13}-1}{4}$

A inequality proposed at Zhautykov Olympiad 2008

Chained substitutions of an application in $\lambda$-calculus, e.g. $AB[C/x][D/y]$

Quadratic inequality puzzle: Prove$ |cx^2 + bx + a| ≤ 2$ given $|ax^2+bx+c| ≤ 1$

prove this inequality by $abc=1$

Prove the inequality $\sqrt\frac{a}{a+8} + \sqrt\frac{b}{b+8} +\sqrt\frac{c}{c+8} \geq 1$ with the constraint $abc=1$

Solve the ODE $y'=1-\frac{y}{x}$

Prove a trigonometric identity: $\cos^2A+\cos^2B+\cos^2C+2\cos A\cos B\cos C=1$ when $A+B+C=\pi$

Can one integral can give more than one answer one with natural log and other with tan inverse

Evaluate $\int\frac{x^3}{\sqrt{81x^2-16}}dx$ using Trigonometric Substitution

Solutions of the functional equation $f(x+1)= xf(x)$

Python Regex escape operator \ in substitutions & raw strings

Integrate $e^{\frac{x-y}{x+y}}$ over the triangle bounded by $x=0$, $y=0$, and $y=1-x$

Limit $\lim_{n \to \infty} \frac {a_n}{2^{n-1}}=\frac 4{\pi}$ for $a_{n+1}=a_n+\sqrt{1+a_n^2}$ and $a_0=0$

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Given three a-triangle-sidelengths $a,b,c$. Prove that $3\left((a^{2}b(a-b)+b^{2}c(b-c)+c^{2}a(c-a)\right)\geqq b(a+b-c)(a-c)(c-b)$ .

Proving that $\cos\frac{2\pi}{13}+\cos\frac{6\pi}{13}+\cos\frac{8\pi}{13}=\frac{\sqrt{13}-1}{4}$

A inequality proposed at Zhautykov Olympiad 2008

Chained substitutions of an application in $\lambda$-calculus, e.g. $AB[C/x][D/y]$

Quadratic inequality puzzle: Prove$ |cx^2 + bx + a| ≤ 2$ given $|ax^2+bx+c| ≤ 1$

prove this inequality by $abc=1$

Prove the inequality $\sqrt\frac{a}{a+8} + \sqrt\frac{b}{b+8} +\sqrt\frac{c}{c+8} \geq 1$ with the constraint $abc=1$

Solve the ODE $y'=1-\frac{y}{x}$

Prove a trigonometric identity: $\cos^2A+\cos^2B+\cos^2C+2\cos A\cos B\cos C=1$ when $A+B+C=\pi$

Can one integral can give more than one answer one with natural log and other with tan inverse

Evaluate $\int\frac{x^3}{\sqrt{81x^2-16}}dx$ using Trigonometric Substitution

Solutions of the functional equation $f(x+1)= xf(x)$

Python Regex escape operator \ in substitutions & raw strings

Integrate $e^{\frac{x-y}{x+y}}$ over the triangle bounded by $x=0$, $y=0$, and $y=1-x$

Limit $\lim_{n \to \infty} \frac {a_n}{2^{n-1}}=\frac 4{\pi}$ for $a_{n+1}=a_n+\sqrt{1+a_n^2}$ and $a_0=0$